+0

# Counting

+1
79
2

How many rectangles are in this figure? Each angle is a right angle.

Jan 24, 2022

#1
+1382
+1

Count it by shape:

length x width

1 x 1: 12

1 x 2: 9

1 x 3: 6

1 x 4: 3

2 x 1: 8

2 x 2: 6

2 x 3: 4

2 x 4: 2

3 x 1: 4

3 x 2: 3

3 x 3: 2

3 x 4: 1

Add everything up, and you get 60.

Jan 24, 2022
#2
+516
-1

If you consider the "squares" as rectangles, then we can count the number of rectangle sizes there are.

For the size 1x1 there are 12 squares/rectangles.

For the next size which is a 2 x 1, there are 17 rectangles.

For the next size which is a 3 x 1, there are 10 of those rectangles.

For the next size which is a 4 x 1, there are 3 of those rectangles.

For the next size which is a 2 x 2, there are 6 of those squares/rectangles.

For the next size which is 2 x 3, there are 7 of those rectangles.

For the next size which is 2 x 4, there are 2 of those rectangles.

For the next size which is 3 x 4, there is 1 rectangle.

For the last size which is 3 x 3, there are 2 of those squares/rectangles.

Altogether there are 40 rectangles and 20 squares. (You might count squares as rectangles.)

Jan 24, 2022